Apilot flew a 400-mile flight in 2.5 hours flying into the wind. flying the same rate and with the same wind speed, the return trip took only 2 hours, with a tailwind. what was the speed of the wind? miles per hour

Distance=speed times time

we will do
s=speed of plane in no wind
w=wind speed
t=time

the distance remains the same, it is 400
so first 2.5 hours flying into the wind
means with resistance from wind
400=(s-w)2.5
divide both sides by 2.5
160=s-w

2 hours is return, with help from wind
400=(s+w)2
divide both sides by 2
200=s+w

so we gots
160=s-w
and
200=s+w
add them

160=s-w
200=s+w +
360=2s+0w

360=2s
divide both sides by 2
180=s
so
160=s-w
160=180-w
minus 180 both sides
-20=-w
20=w

wind speed was 20mph
e

Let p be the speed of the plane, and w be the speed of the wind. Then:
400/p-w=2.5
400/p+w=2
2.5p-2.5w=400
2p+2w=400
then:
5p-5w=800
5p+5w=1000
10p=1800
p=180
w=20
The plane flies at 180 mph; the wind blow at 20 mph. ☺☺☺☺

Where’s the